## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 48

Page 1220

It is clear that G(S, 27, v) is a linear manifold in the space M(S, 27, v) of all v-

measurable functions on S and that a set of functions in G(S, 27, v) is

The linear ...

It is clear that G(S, 27, v) is a linear manifold in the space M(S, 27, v) of all v-

measurable functions on S and that a set of functions in G(S, 27, v) is

**linearly****independent**in M(S, 27, v) if and only if it is**linearly independent**in G(S, 27, v).The linear ...

Page 1306

The following table gives the number of

= 0 square integrable at a or b when J{X) ^ 0. There are four possibilities as

shown by the discussion above. Number of

The following table gives the number of

**linearly independent**solutions of (t— A) a= 0 square integrable at a or b when J{X) ^ 0. There are four possibilities as

shown by the discussion above. Number of

**linearly independent**solutions ...Page 1311

The operator T = T(r) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k

= 1, . . ., k; i.e., T is the restriction of 7\(t) (cf. Definition 2.8) to the submanifold of ...

The operator T = T(r) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k

**linearly independent**boundary conditions Bt(f) = 0, i= 1, . . ., k; i.e., T is the restriction of 7\(t) (cf. Definition 2.8) to the submanifold of ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero